Ex 2.5,2 - Class 9

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Ex 2.5, 2 Evaluate the following products without multiplying directly: 103 × 107 103 × 107 = (100 + 3) (100 + 7) Using Identity (x + a) (x + b) = x2 + (a + b)x + ab, where x = 100 , a = 3, b = 7, = (100)2 + (3 + 7) 100 + (3) (7) = 10000 + (10)(100) + 21 = 10000 + 1000 + 21 = 11021 Ex 2.5, 2 Evaluate the following products without multiplying directly: (ii) 95 × 96 95 × 96 = (100 − 5) (100 − 4) Using Identity (x + a) (x + b) = x2 + (a + b)x + ab, where x = 100 , a = –5, b = –4 , = (100)2 + (− 5 − 4) 100 + (− 5) (− 4) = 10000 + (–9)(100) + 20 = 10000 − 900 + 20 = 9120 Ex 2.5, 2 Evaluate the following products without multiplying directly: (iii) 104 × 96 104 × 96 = (100 + 4) (100 − 4) Using the identity  (x + y) (x – y) = x2 – y2 where x = 100 , y = 4 = (100)2 − (4)2  = 10000 − 16 = 9984